Ultraviolet behaviour of higher spin gauge field propagators and one loop mass renormalization

The ultraviolet singular structure of the bulk-to-bulk propagators for higher spin gauge fields in $Ad{S}_4$ space is analyzed in details. Possible interactions with the Higgs scalar and the corresponding one loop mass renormalization are studied. This mass renormalization is finite and connected with the anomalous dimensions of those currents in the corresponding boundary $CF{T}_3$ that cease to be conserved when the interaction is switched on. In particular it is proportional to $\mathrm{\ell }-2$.